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Doris Schattschneider • Michele Emmer (Editors)

M.C. Eschar's Legacy

A Centennial Celebration

Collection of articles coming from the M.C. Escher Centennial Conference, 1998

|y Springer Contents

Preface Doris Schattschneider Celebrating Escher V Michelle Emmer Escher, in Rome, Again IX

Escher's World H.S.M. Coxeter Escher's Fondness for Animals 1 Bruno Ernst (Hans de Rijk) Selection is Distortion 5 Michele Emmer Ravello: An Escherian Place 17 Douglas R. Hofstadter Mystery, Classicism, Elegance: an Endless Chase After Magic .... 24 J. Taylor HoUist and Doris Schattschneider M.C. Escher and C.v.S. Roosevelt 52 Anne Hughes Escher's Sense of Wonder 63 Claude Lamontagne In Search of M.C. Escher's Metaphysical Unconscious 69 Marjorie Senechal Parallel Worlds: Escher and Mathematics, Revisited 83 Mark Veldhuysen M.C. Escher in : The Trail Back 92 XIV Contents

Escher's Artistic Legacy S. Jan Abas Islamic Patterns: The Spark in Escher's 100 Victor Acevedo Space Time with M.C. Escher and R. Buckminster Fuller 113 Sandro Del Prete Between Illusion and Reality 125 Jos De Mey After M.C. Escher 130 Michele Emmer M.C. Escher: , Math, and Cinema 142 Tamas F. Farkas Organic Structures Related to M.C. Escher's Work 150 Robert Fathauer Extending Escher's Recognizable-Motif Tilings to Multiple-Solution Tilings and Tilings 154 with Claire Ferguson A Circle Limit in Stone 166 Kelly M.Houle Portrait of Escher: Behind the 175 Eva Knoll Life After Escher: A (Young) Artist's Journey 189 Mat juska Teja Krasek Sharing some Common Interests of M.C. Escher 199 Makoto Nakamura New Expressions in Tessellating Art: Layered Three-Dimensional 207 Istvan Orosz The of the Master 215 Peter Raedschelders Tilings and Other Unusual Escher-Related Prints 230 Marjorie Rice Escher-Like Patterns from Pentagonal Tilings 244 Contents XV

Rinus Roelofs Not the Tiles, but the Joints: A little Bridge Between M.C. Escher and Leonardo 252 Claudio Seccaroni and Marco Spesso Architecture, and Scenography in the Graphic Work of M.C. Escher: From Vredeman de Vries to Luca Ronconi 265 Richard A. Termes Hand with Reflective Sphere to Six-Point Perspective Sphere 275

Escher's Scientific and Educational Legacy Douglas Dunham Families of Escher Patterns 286 H.S.M. Coxeter The Trigonometry of Escher's Woodcut Circle Limit III 297 Jill Britton Escher in the Classroom 305 Victor J. Donnay Chaotic Geodesic Motion: An Extension of M.C. Escher's Circle Limit Designs 318 Jane Eisenstein and Arthur L. Loeb Rotations and Notations 334 George Escher Folding Rings of Eight Cubes 343 Istvan Hargittai Dethronement of the Plane 353 Scott Kim Computer Games Based on Escher's Spatial Illusions 366 Vladimir A. Koptsik Escher's World: Structure, Symmetry, Sense 379 Kevin Lee Adapting Escher's Rules for "Regular Division of the Plane" to Create TesselMania!® 393 Jean-Frangois Leger M.C. Escher at the Museum: An Educator's Perspective 408 XVI Contents

John F. Rigby Escher, Napoleon, Fermat, and the Nine-point Centre 420 Marjorie Senechal The Symmetry Mystique 427 Valentin E. Vulihman Escher-Like Tessellations on Spherical Models 442

Solution to Scott Kim's puzzle 448

About the Authors 449